Question

What is the maximum value that the graph of `z=10-12w-2w^2`?

Answer 1

maximum value: `color(green)(28)`

Explanation:

Given
`color(white)("XXX")z=10-12w-2w^2`

The vertex will occur at the point where
`color(white)("XXX")(dz)/(dw)=0`
and since the coefficient of `w^2` is negative, the vertex sill be a maximum

In this case `(dz)/(dw)= -12-4w`
so the maximum will occur when `w=-3`
and `z=10-12 * (-3) - 2 * (-3)^2`
`color(white)("XXX")=10+36-18`
`color(white)("XXX")=28`